Molecular picture of electric double layers with weakly adsorbed water

Water adsorption energy, Eads, is a key physical quantity in sustainable chemical technologies such as (photo)electrocatalytic water splitting, water desalination, and water harvesting. In many of these applications, the electrode surface is operated outside the point (potential) of zero charge, which attracts counter-ions to form the electric double layer and controls the surface properties. Here, by applying density functional theory-based finite-field molecular dynamics simulations, we have studied the effect of water adsorption energy Eads on surface acidity and the Helmholtz capacitance of BiVO4 as an example of metal oxide electrodes with weakly chemisorbed water. This allows us to establish the effect of Eads on the coordination number, the H-bond network, and the orientation of chemisorbed water by comparing an oxide series composed of BiVO4, TiO2, and SnO2. In particular, it is found that a positive correlation exists between the degree of asymmetry ΔCH in the Helmholtz capacitance and the strength of Eads. This correlation is verified and extended further to graphene-like systems with physisorbed water, where the electric double layers (EDLs) are controlled by electronic charge rather than proton charge as in the oxide series. Therefore, this work reveals a general relationship between water adsorption energy Eads and EDLs, which is relevant to both electrochemical reactivity and the electrowetting of aqueous interfaces.

Orientational dynamics of the water layer adjacent to Au surface accelerated by polarization effect

The orientation and rearrangement of water on a gold electrode significantly influences its physicochemical heterogeneous performance. Despite numerous experimental and theoretical studies aimed at uncovering the structural characteristics of interfacial water, the orientational behavior resulting from electrode-induced rearrangements remains a subject of ongoing debate. Here, we employed molecular dynamics simulations to investigate the adaptive structure and dynamics properties of interfacial water on Au(111) and Au(100) surfaces by considering a polarizable model for Au atoms in comparison with the non-polarizable model. Compared to the nonpolarizable systems, the polarization effect can enhance the interaction between water molecules and the gold surface. Unexpectedly, the rotational dynamics directly associated with the orientational behavior of water adjacent to the gold surface is accelerated, thereby reducing the hydrogen bond lifetime. The underlying mechanism for this anomalous phenomenon originates from the polarization effect, which induces the attraction of the positive hydrogen atoms to the surface by the negative image charge. This leads to a change in orientation that disrupts the hydrogen bonds in the first water layer and subsequently accelerates reorientation dynamics of water molecules adjacent to the gold surface. These results shed light on the intricate interplay between polarization effects and water molecule dynamics on metal surfaces, establishing the foundation for the rational regulation of the orientation of interfacial water.

Understanding electrochemical interfaces through comparing experimental and computational charge density-potential curves

Electrode-electrolyte interfaces play a decisive role in electrochemical charge accumulation and transfer processes. Theoretical modelling of these interfaces is critical to decipher the microscopic details of such phenomena. Different force field-based molecular dynamics protocols are compared here in a view to connect calculated and experimental charge density-potential relationships. Platinum-aqueous electrolyte interfaces are taken as a model. The potential of using experimental charge density-potential curves to transform cell voltage into electrode potential in force-field molecular dynamics simulations, and the need for that purpose of developing simulation protocols that can accurately calculate the double-layer capacitance, are discussed.

Reactive molecular dynamics simulations of lithium-ion battery electrolyte degradation

The development of reliable computational methods for novel battery materials has become essential due to the recently intensified research efforts on more sustainable energy storage materials. Here, we use a recently developed framework allowing to consistently incorporate quantum-mechanical activation barriers to classical molecular dynamics simulations to study the reductive solvent decomposition and formation of the solid electrolyte interphase for a graphite/carbonate electrolyte interface. We focus on deriving condensed-phase effective rates based on the elementary gas-phase reduction and decomposition energy barriers. After a short initial transient limited by the elementary barriers, we observe that the effective rate shows a transition to a kinetically slow regime influenced by the changing coordination environment and the ionic fluxes between the bulk electrolyte and the interface. We also discuss the impact of the decomposition on the ionic mobility. Thus, our work shows how elementary first-principles properties can be mechanistically leveraged to provide fundamental insights into electrochemical stability of battery electrolytes.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

Impedance of nanocapacitors from molecular simulations to understand the dynamics of confined electrolytes

Nanoelectrochemical devices have become a promising candidate technology across various applications, including sensing and energy storage, and provide new platforms for studying fundamental properties of electrode/electrolyte interfaces. In this work, we employ constant-potential molecular dynamics simulations to investigate the impedance of gold-aqueous electrolyte nanocapacitors, exploiting a recently introduced fluctuation-dissipation relation. In particular, we relate the frequency-dependent impedance of these nanocapacitors to the complex conductivity of the bulk electrolyte in different regimes, and use this connection to design simple but accurate equivalent circuit models. We show that the electrode/electrolyte interfacial contribution is essentially capacitive and that the electrolyte response is bulk-like even when the interelectrode distance is only a few nanometers, provided that the latter is sufficiently large compared to the Debye screening length. We extensively compare our simulation results with spectroscopy experiments and predictions from analytical theories. In contrast to experiments, direct access in simulations to the ionic and solvent contributions to the polarization allows us to highlight their significant and persistent anticorrelation and to investigate the microscopic origin of the timescales observed in the impedance spectrum. This work opens avenues for the molecular interpretation of impedance measurements, and offers valuable contributions for future developments of accurate coarse-grained representations of confined electrolytes.

Coordination Behavior of a Confined Ionic Liquid in Carbon Nanotubes from Molecular Dynamics Simulations

To understand the behavior of ionic liquids (ILs) at carbon material, i.e., carbon nanotube (CNT)-containing pores, we simulated different systems and analyzed their structural─in particular their coordination─behavior as well as their velocity distribution. The extension of our analysis tool CONAN presented here allowed us to study the coordination behavior as a function of the distance to the carbon material. Our systems were composed of three different CNTs combined with either the neat IL 1-ethyl-3-methylimidazolium tetrafluoroborate or with their NaBF4 salt mixtures. We investigated the impact of the force field charge scaling. As previously detected, the neat IL assumed radial layers within the confinement, with the radial density distribution depending strongly on the pore size. For the salt mixtures, the sodium cation remained in the bulk and was observed only once inside a tube. In all systems, the ions showed an overall decreased coordination behavior for regions in the bulk phase close to the carbon pore and within the confinement. The coordination number was always reduced with scaled charges. For charge scaling, higher dynamics was observed also in confinement. Interestingly, the average velocity of the atoms near the surface inside the confined space was higher than that in the center of the pore.

S.O.S: Shape, orientation, and size tune solvation in electrocatalysis

Current models to understand the reactivity of metal/aqueous interfaces in electrochemistry, e.g., volcano plots, are based on the adsorption free energies of reactants and products, which are often small hydrophobic molecules (such as in CO2 and N2 reduction). Calculations played a major role in the quantification and comprehension of these free energies in terms of the interactions that the reactive species form with the surface. However, solvation free energies also come into play in two ways: (i) by modulating the adsorption free energy together with solute-surface interactions, as the solute has to penetrate the water adlayer in contact with the surface and get partially desolvated (which costs free energy); (ii) by regulating transport across the interface, i.e., the free energy profile from the bulk to the interface, which is strongly non-monotonic due to the unique nature of metal/aqueous interfaces. Here, we use constant potential molecular dynamics to study the solvation contributions, and we uncover huge effects of the shape and orientation (on top of the already known size effect) of small hydrophobic and amphiphilic solutes on their adsorption free energy. We propose a minimal theoretical model, the S.O.S. model, that accounts for size, orientation, and shape effects. These novel aspects are rationalized by recasting the concepts at the base of the Lum-Chandler-Weeks theory of hydrophobic solvation (for small solutes in the so-called volume-dominated regime) into a layer-by-layer form, where the properties of each interfacial region close to the metal are explicitly taken into account.

Differential Capacitance of Ionic Liquid Confined between Metallic Interfaces

We present here a detailed analysis of the electric double layer at the gold electrode/[BMIM][BF4] interface using a polarizable model for the electrode, based on our recent approach to include image charges [Geada et al. Nat. Commun. 2018, 9, 716]. A double bell (camel) shape is obtained for the differential capacitance, where the inclusion of metal polarization allows for a higher density of ions in the double layer, particularly around the maxima, thereby increasing the capacitance. The charging mechanism differs for the positive and negative electrodes, with counterion adsorption prevailing at the anode and co-ion desorption prevailing at the cathode. The charging mechanism is predominantly governed by the BF4 anions, serving as counterions and co-ions at the anode and cathode, respectively. Within the considered range of potentials, only minor changes are observed in the dynamical properties, specifically in the diffusion coefficients. Notably, it is interesting to observe that bulk properties are restored at a shorter distance from the gold surface in the case of the anode compared to the cathode.

Solvent-dependent iodide interactions in LiO2 electrolytes - a molecular dynamics study

Iodide-based redox mediation in Li-O2 batteries is regarded as a promising system due to its relatively high round-trip efficiency, compared to alternative systems. Here we explore the role of electrolyte composition in the solvation of I-, which has been shown to be critical for the efficient operation of this redox mediator, using a molecular dynamics approach. A combinatorial exploration of I- and H2O concentrations was performed, for a fixed concentration of Li+, across a series of glymes, with increasing chain length (mono- to tetraglyme). The resulting radial distribution functions show that shorter glymes allow for a closer packing of the I- redox mediator. Furthermore, increasing the I- concentration also reduces the solvation of Li+ in the glymes, especially in G2. The presence of water further pulls the I- and Li+ together. With increasing water content, its presence in the iodide's coordination shell increases markedly - an effect most pronounced for monoglyme. Competition between Li+ and I- for the coordination of water is modulated by the different solvents as they perturb the local coordination shell of these important complexes, with longer chain lengths being less affected by increases in water concentrations.

Charging and discharging a supercapacitor in molecular simulations

As the world moves more toward unpredictable renewable energy sources, better energy storage devices are required. Supercapacitors are a promising technology to meet the demand for short-term, high-power energy storage. Clearly, understanding their charging and discharging behaviors is essential to improving the technology. Molecular Dynamics (MD) simulations provide microscopic insights into the complex interplay between the dynamics of the ions in the electrolyte and the evolution of the charge distributions on the electrodes. Traditional MD simulations of (dis)charging supercapacitors impose a pre-determined evolving voltage difference between the electrodes, using the Constant Potential Method (CPM). Here, we present an alternative method that explicitly simulates the charge flow to and from the electrodes. For a disconnected capacitor, i.e., an open circuit, the charges are allowed to redistribute within each electrode while the sum charges on both electrodes remain constant. We demonstrate, for a model capacitor containing an aqueous salt solution, that this method recovers the charge-potential curve of CPM simulations. The equilibrium voltage fluctuations are related to the differential capacitance. We next simulate a closed circuit by introducing equations of motion for the sum charges, by explicitly accounting for the external circuit element(s). Charging and discharging of the model supercapacitor via a resistance proceed by double exponential processes, supplementing the usual time scale set by the electrolyte dynamics with a novel time scale set by the external circuit. Finally, we propose a simple equivalent circuit that reproduces the main characteristics of this supercapacitor.

A simple efficient algorithm for molecular simulations of constant potential electrodes

Increasingly, society requires high power, high energy storage devices for applications ranging from electric vehicles to buffers on the electric grid. Supercapacitors are a promising contribution to meeting these demands, though there still remain unsolved practical problems. Molecular dynamics simulations can shed light on the relevant molecular level processes in electric double layer capacitors, but these simulations are computationally very demanding. Our focus here is on the algorithmic complexity of the constant potential method (CPM), which uses dedicated electrostatics solvers to maintain a fixed potential difference between two conducting electrodes. We show how any standard electrostatics solver-capable of calculating the energies and forces on all atoms-can be used to implement CPM with a minimum of coding. As an example, we compare our generalized implementation of CPM, based on invocations of the particle-particle-particle-mesh routine of the Large-scale Atomic/Molecular Massively Parallel Simulator, with a traditional implementation based on a dedicated re-implementation of Ewald summation. Both methods yield comparable results on four test systems, with the former achieving a substantial gain in speed and improved scalability. The step from dedicated electrostatic solvers to generic routines is made possible by noting that CPM's traditional narrow Gaussian point-spread of atomic charges on the electrodes effectively endows point-like atoms with chemical hardness, i.e., an intra-atomic energy quadratic in the charge.

Developing an Implicit Solvation Machine Learning Model for Molecular Simulations of Ionic Media

Molecular dynamics (MD) simulations of biophysical systems require accurate modeling of their native environment, i.e., aqueous ionic solution, as it critically impacts the structure and function of biomolecules. On the other hand, the models should be computationally efficient to enable simulations of large spatiotemporal scales. Here, we present the deep implicit solvation model for sodium chloride solutions that satisfies both requirements. Owing to the use of the neural network potential, the model can capture the many-body potential of mean force, while the implicit water treatment renders the model inexpensive. We demonstrate our approach first for pure ionic solutions with concentrations ranging from physiological to 2 M. We then extend the model to capture the effective ion interactions in the vicinity and far away from a DNA molecule. In both cases, the structural properties are in good agreement with all-atom MD, showcasing a general methodology for the efficient and accurate modeling of ionic media.

Negative Dielectric Constant of Water at a Metal Interface

Water polarizability at a metal interface plays an essential role in electrochemistry. We devise a classical molecular dynamics approach with an efficient description of metal polarization and a novel ac field method to measure the local dielectric response of interfacial water. Water adlayers next to the metal surface exhibit higher-than-bulk in-plane and negative out-of-plane dielectric constants, the latter corresponding physically to overscreening of the applied field. If we account for the gap region at the interface, the average out-of-plane dielectric constant is quite low (ε_{⊥}≈2), in agreement with reported measurements on confined thin films.

Self-assembling biomolecules for biosensor applications

Molecular self-assembly has received considerable attention in biomedical fields as a simple and effective method for developing biomolecular nanostructures. Self-assembled nanostructures can exhibit high binding affinity and selectivity by displaying multiple ligands/receptors on their surface. In addition, the use of supramolecular structure change upon binding is an intriguing approach to generate binding signal. Therefore, many self-assembled nanostructure-based biosensors have been developed over the past decades, using various biomolecules (e.g., peptides, DNA, RNA, lipids) and their combinations with non-biological substances. In this review, we provide an overview of recent developments in the design and fabrication of self-assembling biomolecules for biosensing. Furthermore, we discuss representative electrochemical biosensing platforms which convert the biochemical reactions of those biomolecules into electrical signals (e.g., voltage, ampere, potential difference, impedance) to contribute to detect targets. This paper also highlights the successful outcomes of self-assembling biomolecules in biosensor applications and discusses the challenges that this promising technology needs to overcome for more widespread use.

CONAN─Novel Tool to Create and Analyze Liquids in Confined Space

Modeling of complex liquids at solid surfaces and in confinement is gaining attention due to an increase in computer power and advancement of simulation techniques. Therefore, tools to set up structures and for analysis are needed. In this paper, we present CONAN─a Python code designed to facilitate the study of liquids interacting with solid structures, such as walls or pores. Among other things, the program provides the option to generate a variety of different structures, including carbon walls and nanotubes and their boron nitride analogs, as well as the ability to analyze various structural properties of confined and interfacial liquids. In the case of the ionic liquid 1-butyl-3-methylimidazolium acetate in carbon nanotubes of different sizes, we demonstrate the abilities of our tool. The average density within the confinement highly depends on the carbon nanotube size, and it is generally lower than the density of the bulk liquid. The arrangement of the individual species within the tube also depends on size, with radial layers forming within the tubular confinement. The density is largely increased in the respective layers, while it is drastically reduced between the layers.

Unified quantum theory of electrochemical kinetics by coupled ion-electron transfer

A general theory of coupled ion-electron transfer (CIET) is presented, which unifies Marcus kinetics of electron transfer (ET) with Butler-Volmer kinetics of ion transfer (IT). In the limit of large reorganization energy, the theory predicts normal Marcus kinetics of "electron-coupled ion transfer" (ECIT). In the limit of large ion transfer energies, the theory predicts Butler-Volmer kinetics of "ion-coupled electron transfer" (ICET), where the charge transfer coefficient and exchange current are connected to microscopic properties of the electrode/electrolyte interface. In the ICET regime, the reductive and oxidative branches of Tafel's law are predicted to hold over a wide range of overpotentials, bounded by the ion-transfer energies for oxidation and reduction, respectively. The probability distribution of transferring electron energies in CIET smoothly interpolates between a shifted Gaussian distribution for ECIT (as in the Gerischer-Marcus theory of ET) to an asymmetric, fat-tailed Meixner distribution centered at the Fermi level for ICET. The latter may help interpret asymmetric line shapes in x-ray photo-electron spectroscopy (XPS) and Auger electron spectroscopy (AES) for metal surfaces in terms of shake-up relaxation of the ionized atom and its image polaron by ICET. In the limit of large overpotentials, the theory predicts a transition to inverted Marcus ECIT, leading to a universal reaction-limited current for metal electrodes, dominated by barrierless quantum transitions. Uniformly valid, closed-form asymptotic approximations are derived that smoothly transition between the limiting rate expressions for ICET and ECIT for metal electrodes, using simple but accurate mathematical functions. The theory is applied to lithium intercalation in lithium iron phosphate (LFP) and found to provide a consistent description of the observed current dependence on overpotential, temperature and concentration. CIET theory thus provides a critical bridge between quantum electrochemistry and electrochemical engineering, which may find many other applications and extensions.

Nanoscale probing of local dielectric changes at the interface between solids and aqueous saline solutions

The mobility of dissolved ions and charged molecules at interfaces underpins countless processes in science and technology. Experimentally, this is typically measured from the averaged response of the charges to an electrical potential. High-resolution Atomic Force Microscopy (AFM) can image single adsorbed ions and molecules at solid-liquid interfaces, but probing the associated dynamics remains highly challenging. One possible strategy is to investigate the response of the species of interest to a highly localized AC electric field in an approach analogous to dielectric spectroscopy. The dielectric force experienced by the AFM tip apex is modulated by the dielectric properties of the sample probed, itself sensitive to the mobilities of solvated charges and dipoles. Previous work successfully used this approach to quantify the dielectric constant of thin samples, but with limited spatial resolution. Here we propose a strategy to simultaneously map the nanoscale topography and local dielectric variations across a range of interfaces by conducting high-resolution AFM imaging concomitantly with electrical AC measurements in a multifrequency approach. The strategy is tested over a 500 MHz bandwidth in pure liquids with different dielectric constants and in saline aqueous solutions. In liquids with higher dielectric constants, the system behaves as inductive-resistive-capacitive but the adjunction of ions removes the inductive resonances and precludes measurements at higher frequencies. High-resolution imaging is demonstrated over single graphene oxide (GrO) flakes with simultaneous but decoupled dielectric measurements. The dielectric constant is consistent and reproducible across liquids, except at higher salt concentrations where frequency-dependent effects occur. The results suggest the strategy is suitable for nanometre-level mapping of the dielectric properties of solid-liquid interfaces, but more work is needed to fully understand the different physical effects underpinning the measurements.

Electrical noise in electrolytes: a theoretical perspective

Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and surface force balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization, the field gradient (for quadrupolar nuclei) and the coupled mass/charge densities. The fluctuations of such various observables arise from the same underlying microscopic dynamics of the ions and solvent molecules. In principle, the relevant length and time scales of these dynamics are encoded in the dynamic structure factors. However, modelling the latter for frequencies and wavevectors spanning many orders of magnitude remains a great challenge to interpret the experiments in terms of physical processes such as solvation dynamics, diffusion, electrostatic and hydrodynamic interactions between ions, interactions with solid surfaces, etc. Here, we highlight the central role of the charge-charge dynamic structure factor in the fluctuations of electrical observables in electrolytes and offer a unifying perspective over a variety of complementary experiments. We further analyze this quantity in the special case of an aqueous NaCl electrolyte, using simulations with explicit ions and an explicit or implicit solvent. We discuss the ability of the standard Poisson-Nernst-Planck theory to capture the simulation results, and how the predictions can be improved. We finally discuss the contributions of ions and water to the total charge fluctuations. This work illustrates an ongoing effort towards a comprehensive understanding of electrical fluctuations in bulk and confined electrolytes, in order to enable experimentalists to decipher the microscopic properties encoded in the measured electrical noise.

Molecular dynamics simulations of electrified interfaces including the metal polarisation

Understanding electrified interfaces requires an accurate description of the electric double layer which also takes into account the metal polarisation. Here we present a simple approach to the molecular dynamics simulation of electrified interfaces which combines fixed charges and a core-shell model for the description of the polarisable electron density on the metal electrode. The approach has been applied to the Au(111) surface in contact with a NaCl aqueous electrolyte solution in order to calculate the differential capacitance and to gain a detailed picture of the charging mechanism. Metal polarisation enhances the interfacial capacitance with a difference between the cathode and anode. In particular, we find that the influence of the metal polarisation on the electric double layer depends on the ion's solvation shell structure and, for the investigated interface, is more important at the cathode, where it modifies the sodium ion distribution.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations

Using Brownian dynamics simulations, we investigate the effects of confinement, adsorption on surfaces, and ion-ion interactions on the response of confined electrolyte solutions to oscillating electric fields in the direction perpendicular to the confining walls. Nonequilibrium simulations allows to characterize the transitions between linear and nonlinear regimes when varying the magnitude and frequency of the applied field, but the linear response, characterized by the frequency-dependent conductivity, is more efficiently predicted from the equilibrium current fluctuations. To that end, we (rederive and) use the Green-Kubo relation appropriate for overdamped dynamics, which differs from the standard one for Newtonian or underdamped Langevin dynamics. This expression highlights the contributions of the underlying Brownian fluctuations and of the interactions of the particles between them and with external potentials. Although already known in the literature, this relation has rarely been used to date, beyond the static limit to determine the effective diffusion coefficient or the DC conductivity. The frequency-dependent conductivity always decays from a bulk-like behavior at high frequency to a vanishing conductivity at low frequency due to the confinement of the charge carriers by the walls. We discuss the characteristic features of the crossover between the two regimes, most importantly how the crossover frequency depends on the confining distance and the salt concentration, and the fact that adsorption on the walls may lead to significant changes both at high and low frequencies. Conversely, our results illustrate the possibility to obtain information on diffusion between walls, charge relaxation, and adsorption by analyzing the frequency-dependent conductivity.

Frequency-Dependent Impedance of Nanocapacitors from Electrode Charge Fluctuations as a Probe of Electrolyte Dynamics

The frequency-dependent impedance is a fundamental property of electrical components. We show that it can be determined from the equilibrium dynamical fluctuations of the electrode charge in constant-potential molecular simulations, extending in particular a fluctuation-dissipation relation for the capacitance recovered in the low-frequency limit and provide an illustration on water-gold nanocapacitors. This Letter opens the way to the interpretation of electrochemical impedance measurements in terms of microscopic mechanisms, directly from the dynamics of the electrolyte, or indirectly via equivalent circuit models as in experiments.

Insight into the Interaction of Furfural with Metallic Surfaces in the Electrochemical Hydrogenation Process

Electrocatalytic hydrogenation of furfural on metal surfaces has become an important research subject due to the potential of the reaction product 2-methylfuran as a renewable energy resource. Identifying effective determinants in this reaction process requires a thorough investigation of the complex electrode-electrolyte interactions, which considers a variety of the influential components. In this work, in operando electrochemical Raman Spectroscopy and Molecular Dynamics simulations were utilized to investigate different characteristics of the interface layer in the electrocatalytic hydrogenation of furfural. Hereby, the influence of applied potentials, electrode material, and electrolyte composition were investigated in detail. The studied parameters give an insight into furfural's binding situation, molecular orientation, and reaction mechanism.

Coupled Interactions at the Ionic Graphene-Water Interface

We compute ionic free energy adsorption profiles at an aqueous graphene interface by developing a self-consistent approach. To do so, we design a microscopic model for water and put the liquid on an equal footing with the graphene described by its electronic band structure. By evaluating progressively the electronic and dipolar coupled electrostatic interactions, we show that the coupling level including mutual graphene and water screening permits one to recover remarkably the precision of extensive quantum simulations. We further derive the potential of mean force evolution of several alkali cations.

Predictive Molecular Models for Charged Materials Systems: From Energy Materials to Biomacromolecules

Electrostatic interactions play a dominant role in charged materials systems. Understanding the complex correlation between macroscopic properties with microscopic structures is of critical importance to develop rational design strategies for advanced materials. But the complexity of this challenging task is augmented by interfaces present in the charged materials systems, such as electrode-electrolyte interfaces or biological membranes. Over the last decades, predictive molecular simulations that are founded in fundamental physics and optimized for charged interfacial systems have proven their value in providing molecular understanding of physicochemical properties and functional mechanisms for diverse materials. Novel design strategies utilizing predictive models have been suggested as promising route for the rational design of materials with tailored properties. Here, an overview of recent advances in the understanding of charged interfacial systems aided by predictive molecular simulations is presented. Focusing on three types of charged interfaces found in energy materials and biomacromolecules, how the molecular models characterize ion structure, charge transport, morphology relation to the environment, and the thermodynamics/kinetics of molecular binding at the interfaces is discussed. The critical analysis brings two prominent field of energy materials and biological science under common perspective, to stimulate crossover in both research field that have been largely separated.

Co-Ion Desorption as the Main Charging Mechanism in Metallic 1T-MoS2 Supercapacitors

Metallic 1T-MoS₂ is a promising electrode material for supercapacitor applications. Its layered structure allows the efficient intercalation of ions, leading to experimental volumetric capacitance as high as 140 F/cm³. Molecular dynamics could in principle be used to characterize its charging mechanism; however, unlike conventional nanoporous carbon, 1T-MoS₂ is a multicomponent electrode. The Mo and S atoms have very different electronegativities so that 1T-MoS₂ cannot be simulated accurately using the conventional constant potential method. In this work, we show that controlling the electrochemical potential of the atoms allows one to recover average partial charges for the elements in agreement with electronic structure calculations for the material at rest, without compromising the ability to simulate systems under an applied voltage. The simulations yield volumetric capacitances in agreement with experiments. We show that due to the large electronegativity of S, the co-ion desorption is the main charging mechanism at play during the charging process. This contrasts drastically with carbon materials for which ion exchange and counterion adsorption usually dominate. In the future, our method can be extended to the study of a wide range of families of 2D layered materials such as MXenes.

ELECTRODE: An electrochemistry package for atomistic simulations

Constant potential methods (CPM) enable computationally efficient simulations of the solid-liquid interface at conducting electrodes in molecular dynamics (MD). They have been successfully used, for example, to realistically model the behavior of ionic liquids or water-in-salt electrolytes in supercapacitors and batteries. The CPM models conductive electrodes by updating charges of individual electrode atoms according to the applied electric potential and the (time-dependent) local electrolyte structure. Here we present a feature-rich CPM implementation, called ELECTRODE, for the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), which includes a constrained charge method and a thermo-potentiostat. The ELECTRODE package also contains a finite-field approach, multiple corrections for non-periodic boundary conditions of the particle-particle particle-mesh solver, and a Thomas-Fermi model for using non-ideal metals as electrodes. We demonstrate the capabilities of this implementation for a parallel-plate electrical double-layer capacitor, for which we have investigated the charging times with the different implemented methods and found an interesting relationship between water and ionic dipole relaxations. To prove the validity of the one-dimensional correction for the long-range electrostatics, we estimated the vacuum capacitance of two co-axial carbon nanotubes and compared it to structureless cylinders, for which an analytical expression exists. In summary, the ELECTRODE package enables efficient electrochemical simulations using state-of-the-art methods, allowing one to simulate even heterogeneous electrodes. Moreover, it allows unveiling more rigorously how electrode curvature affects the capacitance with the one-dimensional correction.

Microscopic Simulations of Electrochemical Double-Layer Capacitors

Electrochemical double-layer capacitors (EDLCs) are devices allowing the storage or production of electricity. They function through the adsorption of ions from an electrolyte on high-surface-area electrodes and are characterized by short charging/discharging times and long cycle-life compared to batteries. Microscopic simulations are now widely used to characterize the structural, dynamical, and adsorption properties of these devices, complementing electrochemical experiments and in situ spectroscopic analyses. In this review, we discuss the main families of simulation methods that have been developed and their application to the main family of EDLCs, which include nanoporous carbon electrodes. We focus on the adsorption of organic ions for electricity storage applications as well as aqueous systems in the context of blue energy harvesting and desalination. We finally provide perspectives for further improvement of the predictive power of simulations, in particular for future devices with complex electrode compositions.

Uncertainty quantification of phase transition quantities from cluster weighting calculations

In this work, we investigate how uncertainties in experimental input data influence the results of quantum cluster equilibrium calculations. In particular, we focus on the calculation of vaporization enthalpies and entropies of seven organic liquids, compare two computational approaches for their calculation and investigate how these properties are affected by changes in the experimental input data. It is observed that the vaporization enthalpies and entropies show a smooth dependence on changes in the reference density and boiling point. The reference density is found to have only a small influence on the vaporization thermodynamics, whereas the boiling point has a large influence on the vaporization enthalpy but only a small influence on the vaporization entropy. Furthermore we employed the Gauss--Hermite estimator in order to quantify the uncertainty in the thermodynamic functions that stems from inaccuracies in the experimental reference data at the example of the vaporization enthalpy of (\textit{R})-butan-2-ol. We quantify the uncertainty as 30.95~$\cdot$10$^{-3}$~kJ~mol$^{-1}$. Additionally we compare the convergence behaviour and computational effort of the Gauss--Hermite estimator with the Monte Carlo approach and show the superiority of the former. By this, we present how uncertainty quantification can be applied to examples from theoretical chemistry.

Understanding the Electric Double-Layer Structure, Capacitance, and Charging Dynamics

Significant progress has been made in recent years in theoretical modeling of the electric double layer (EDL), a key concept in electrochemistry important for energy storage, electrocatalysis, and multitudes of other technological applications. However, major challenges remain in understanding the microscopic details of the electrochemical interface and charging mechanisms under realistic conditions. This review delves into theoretical methods to describe the equilibrium and dynamic responses of the EDL structure and capacitance for electrochemical systems commonly deployed for capacitive energy storage. Special emphasis is given to recent advances that intend to capture the nonclassical EDL behavior such as oscillatory ion distributions, polarization of nonmetallic electrodes, charge transfer, and various forms of phase transitions in the micropores of electrodes interfacing with an organic electrolyte or ionic liquid. This comprehensive analysis highlights theoretical insights into predictable relationships between materials characteristics and electrochemical performance and offers a perspective on opportunities for further development toward rational design and optimization of electrochemical systems.

Solubilities and Transport Properties of CO2, Oxalic Acid, and Formic Acid in Mixed Solvents Composed of Deep Eutectic Solvents, Methanol, and Propylene Carbonate

Recently, deep eutectic solvents (DES) have been considered as possible electrolytes for the electrochemical reduction of CO₂ to value-added products such as formic and oxalic acids. The applicability of pure DES as electrolytes is hindered by high viscosities. Mixtures of DES with organic solvents can be a promising way of designing superior electrolytes by exploiting the advantages of each solvent type. In this study, densities, viscosities, diffusivities, and ionic conductivities of mixed solvents comprising DES (i.e., reline and ethaline), methanol, and propylene carbonate were computed using molecular simulations. To provide a quantitative assessment of the affinity and mass transport of CO₂ and oxalic and formic acids in the mixed solvents, the solubilities and self-diffusivities of these solutes were also computed. Our results show that the addition of DES to the organic solvents enhances the solubilities of oxalic and formic acids, while the solubility of CO₂ in the ethaline-containing mixtures are in the same order of magnitude with the respective pure organic components. A monotonic increase in the densities and viscosities of the mixed solvents is observed as the mole fraction of DES in the mixture increases, with the exception of the density of ethaline-propylene carbonate which shows the opposite behavior due to the high viscosity of the pure organic component. The self-diffusivities of all species in the mixtures significantly decrease as the mole fraction of DES approaches unity. Similarly, the self-diffusivities of the dissolved CO₂ and the oxalic and formic acids also decrease by at least 1 order of magnitude as the composition of the mixture shifts from the pure organic component to pure DES. The computed ionic conductivities of all mixed solvents show a maximum value for mole fractions of DES in the range from 0.2 to 0.6 and decrease as more DES is added to the mixtures. Since for most mixtures studied here no prior experimental measurements exist, our findings can serve as a first data set based on which further investigation of DES-containing electrolyte solutions can be performed for the electrochemical reduction of CO₂ to useful chemicals.

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

Self-consistent determination of long-range electrostatics in neural network potentials

Machine learning has the potential to revolutionize the field of molecular simulation through the development of efficient and accurate models of interatomic interactions. Neural networks can model interactions with the accuracy of quantum mechanics-based calculations, but with a fraction of the cost, enabling simulations of large systems over long timescales. However, implicit in the construction of neural network potentials is an assumption of locality, wherein atomic arrangements on the nanometer-scale are used to learn interatomic interactions. Because of this assumption, the resulting neural network models cannot describe long-range interactions that play critical roles in dielectric screening and chemical reactivity. Here, we address this issue by introducing the self-consistent field neural network - a general approach for learning the long-range response of molecular systems in neural network potentials that relies on a physically meaningful separation of the interatomic interactions - and demonstrate its utility by modeling liquid water with and without applied fields.

Multi-scale simulation of the adsorption of lithium ion on graphite surface: From quantum Monte Carlo to molecular density functional theory

The structure of the double-layer formed at the surface of carbon electrodes is governed by the interactions between the electrode and the electrolyte species. However, carbon is notoriously difficult to simulate accurately, even with well-established methods such as electronic density functional theory and molecular dynamics. Here, we focus on the important case of a lithium ion in contact with the surface of graphite, and we perform a series of reference quantum Monte Carlo calculations that allow us to benchmark various electronic density functional theory functionals. We then fit an accurate carbon–lithium pair potential, which is used in molecular density functional theory calculations to determine the free energy of the adsorption of the ion on the surface in the presence of water. The adsorption profile in aqueous solution differs markedly from the gas phase results, which emphasize the role of the solvent on the properties of the double-layer.

Elucidating Curvature-Capacitance Relationships in Carbon-Based Supercapacitors

Nanoscale surface curvatures, either convex or concave, strongly influence the charging behavior of supercapacitors. Rationalizing individual influences of electrode atoms to the capacitance is possible by interpreting distinct elements of the charge-charge covariance matrix derived from individual charge variations of the electrode atoms. An ionic liquid solvated in acetonitrile and confined between two electrodes, each consisting of three undulated graphene layers, serves as a demonstrator to illustrate pronounced and nontrivial features of the capacitance with respect to the electrode curvature. In addition, the applied voltage determines whether a convex or concave surface contributes to increased capacitance. While at lower voltages capacitance variations are in general correlated with ion number density variations in the double layer formed in the concave region of the electrode, for certain electrode designs a surprisingly strong contribution of the convex part to the differential capacitance is found both at higher and lower voltages.

Dissolving salt is not equivalent to applying a pressure on water

Salt water is ubiquitous, playing crucial roles in geological and physiological processes. Despite centuries of investigations, whether or not water’s structure is drastically changed by dissolved ions is still debated. Based on density functional theory, we employ machine learning based molecular dynamics to model sodium chloride, potassium chloride, and sodium bromide solutions at different concentrations. The resulting reciprocal-space structure factors agree quantitatively with neutron diffraction data. Here we provide clear evidence that the ions in salt water do not distort the structure of water in the same way as neat water responds to elevated pressure. Rather, the computed structural changes are restricted to the ionic first solvation shells intruding into the hydrogen bond network, beyond which the oxygen radial-distribution function does not undergo major change relative to neat water. Our findings suggest that the widely cited pressure-like effect on the solvent in Hofmeister series ionic solutions should be carefully revisited.

By advanced machine learning techniques, first-principles simulations find that dissolving salt in water does not change water structure drastically. It is contrary to the notion of “pressure effect” which has been widely applied over past 25 years.

An evaluation of the capacitive behavior of supercapacitors as a function of the radius of cations using simulations with a constant potential method

We report on the atomistic molecular dynamics, applying the constant potential method to determine the structural and electrostatic interactions at the electrode-electrolyte interface of electrochemical supercapacitors as a function of the cation radius (Cs⁺, Rb⁺, K⁺, Na⁺, Li⁺). We find that the electrical double layer is susceptible to the size, hydration layer volume, and cations' mobility and analyzed them. Besides, the transient potential shows an increase in magnitude and length as a function of the monocation size, i.e., Cs⁺ > Rb⁺ > K⁺ > Na⁺ > Li⁺. On the other hand, the charge distribution along the electrode surface is less uniform for large monocations. Nonetheless, the difference is not observed as a function of the radius of the cation for the integral capacitance. Our results are comparable to studies that employed the fixed charge method for treating such systems.

Chemistry Dissolved in Ionic Liquids. A Theoretical Perspective

The theoretical treatment of ionic liquids must focus now on more realistic models while at the same time keeping an accurate methodology when following recent ionic liquids research trends or allowing predictability to come to the foreground. In this Perspective, we summarize in three cases of advanced ionic liquid research what methodological progress has been made and point out difficulties that need to be overcome. As particular examples to discuss we choose reactions, chirality, and radicals in ionic liquids. All these topics have in common that an explicit or accurate treatment of the electronic structure and/or intermolecular interactions is required (accurate methodology), while at the same time system size and complexity as well as simulation time (realistic model) play an important role and must be covered as well.

Microscopic origin of the effect of substrate metallicity on interfacial free energies

We investigate the effect of the metallic character of solid substrates on solid-liquid interfacial thermodynamics using molecular simulations. Building on the recent development of a semiclassical Thomas-Fermi model to tune the metallicity in classical molecular dynamics simulations, we introduce a thermodynamic integration framework to compute the evolution of the interfacial free energy as a function of the Thomas-Fermi screening length. We validate this approach against analytical results for empty capacitors and by comparing the predictions in the presence of an electrolyte with values determined from the contact angle of droplets on the surface. The general expression derived in this work highlights the role of the charge distribution within the metal. We further propose a simple model to interpret the evolution of the interfacial free energy with voltage and Thomas-Fermi length, which allows us to identify the charge correlations within the metal as the microscopic origin of the evolution of the interfacial free energy with the metallic character of the substrate. This methodology opens the door to the molecular-scale study of the effect of the metallic character of the substrate on confinement-induced transitions in ionic systems, as reported in recent atomic force microscopy and surface force apparatus experiments.

A molecular perspective on induced charges on a metallic surface

Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode-electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode-electrolyte interfaces.

Modeling galvanostatic charge-discharge of nanoporous supercapacitors

Molecular modeling has been considered indispensable in studying the energy storage of supercapacitors at the atomistic level. The constant potential method (CPM) allows the electric potential to be kept uniform in the electrode, which is essential for a realistic description of the charge repartition and dynamics process in supercapacitors. However, previous CPM studies have been limited to the potentiostatic mode. Although widely adopted in experiments, the galvanostatic mode has rarely been investigated in CPM simulations because of a lack of effective methods. Here we develop a modeling approach to simulating the galvanostatic charge-discharge process of supercapacitors under constant potential. We show that, for nanoporous electrodes, this modeling approach can capture experimentally consistent dynamics in supercapacitors. It can also delineate, at the molecular scale, the hysteresis in ion adsorption-desorption dynamics during charging and discharging. This approach thus enables the further accurate modeling of the physics and electrochemistry in supercapacitor dynamics.

Structural effects in nanotribology of nanoscale films of ionic liquids confined between metallic surfaces

Room Temperature Ionic Liquids (RTILs) attract significant interest in nanotribology. However, their microscopic lubrication mechanism is still under debate. Here, using non-equilibrium molecular dynamics simulations, we investigate the lubrication performance of ultra-thin (<2 nm) films of [C₂MIM]⁺ [NTf₂]^- confined between plane-parallel neutral surfaces of Au(111) or Au(100). We find that films consisting of tri-layers or bilayers, form ordered structures with a flat orientation of the imidazolium rings with respect to the gold surface plane. Tri-layers are unstable against loads >0.5 GPa, while bi-layers sustain pressures in the 1-2 GPa range. The compression of these films results in monolayers that can sustain loads of several GPa without significant loss in their lubrication performance. Surprisingly, in such ultra-thin films the imidazolium rings show higher orientational in-plane disorder, with and the rings adopting a tilted orientation with respect to the gold surface. The friction force and friction coefficient of the monolayers depends strongly on the structure of the gold plates, with the friction coefficient being four times higher for monolayers confined between Au(100) surfaces than for more compact Au(111) surfaces. We show that the general behaviour described here is independent of whether the metallic surfaces are modelled as polarizable or non-polarizable surfaces and speculate on the nature of this unexpected conclusion.

Multifunctional Electrocatalysis on Single-Site Metal Catalysts: A Computational Perspective

Multifunctional electrocatalysts are vastly sought for their applications in water splitting electrolyzers, metal-air batteries, and regenerative fuel cells because of their ability to catalyze multiple reactions such as hydrogen evolution, oxygen evolution, and oxygen reduction reactions. More specifically, the application of single-atom electrocatalyst in multifunctional catalysis is a promising approach to ensure good atomic efficiency, tunability and additionally benefits simple theoretical treatment. In this review, we provide insights into the variety of single-site metal catalysts and their identification. We also summarize the recent advancements in computational modeling of multifunctional electrocatalysis on single-site catalysts. Furthermore, we explain each modeling step with open-source-based working examples of a standard computational approach.

Effect of the metallicity on the capacitance of gold-aqueous sodium chloride interfaces

Electrochemistry experiments have established that the capacitance of electrode-electrolyte interfaces is much larger for good metals, such as gold and platinum, than for carbon-based materials. Despite the development of elaborate electrode interaction potentials, to date molecular dynamics simulations are not able to capture this effect. Here, we show that changing the width of the Gaussian charge distribution used to represent the atomic charges in gold is an effective way to tune its metallicity. Larger Gaussian widths lead to a capacitance of aqueous solutions (pure water and 1 M NaCl) in good agreement with recent ab initio molecular dynamics results. For pure water, the increase in the capacitance is not accompanied by structural changes, while in the presence of salt, the Na⁺ cations tend to adsorb significantly on the surface. For a strongly metallic gold electrode, these ions can even form inner sphere complexes on hollow sites of the surface.

Controlling potential difference between electrodes based on self-consistent-charge density functional tight binding

A proper understanding and description of the electronic response of the electrode surfaces in electrochemical systems are quite important because the interactions between the electrode surface and electrolyte give rise to unique and useful interfacial properties. Atomistic modeling of the electrodes requires not only an accurate description of the electronic response under a constant-potential condition but also computational efficiency in order to deal with systems large enough to investigate the interfacial electrolyte structures. We thus develop a self-consistent-charge density functional tight binding based method to model a pair of electrodes in electrochemical cells under the constant-potential condition. The method is more efficient than the (ab initio) density functional theory calculations so that it can treat systems as large as those studied in classical atomistic simulations. It can also describe the electronic response of electrodes quantum mechanically and more accurately than the classical counterparts. The constant-potential condition is introduced through a Legendre transformation of the electronic energy with respect to the difference in the number of electrons in the two electrodes and their electrochemical potential difference, through which the Kohn-Sham equations for each electrode are variationally derived. The method is applied to platinum electrodes faced parallel to each other under an applied voltage. The electronic response to the voltage and a charged particle is compared with the result of a classical constant-potential method based on the chemical potential equalization principle.

On the Gibbs-Thomson equation for the crystallization of confined fluids

The Gibbs-Thomson (GT) equation describes the shift of the crystallization temperature for a confined fluid with respect to the bulk as a function of pore size. While this century old relation is successfully used to analyze experiments, its derivations found in the literature often rely on nucleation theory arguments (i.e., kinetics instead of thermodynamics) or fail to state their assumptions, therefore leading to similar but different expressions. Here, we revisit the derivation of the GT equation to clarify the system definition, corresponding thermodynamic ensemble, and assumptions made along the way. We also discuss the role of the thermodynamic conditions in the external reservoir on the final result. We then turn to numerical simulations of a model system to compute independently the various terms entering in the GT equation and compare the predictions of the latter with the melting temperatures determined under confinement by means of hyper-parallel tempering grand canonical Monte Carlo simulations. We highlight some difficulties related to the sampling of crystallization under confinement in simulations. Overall, despite its limitations, the GT equation may provide an interesting alternative route to predict the melting temperature in large pores using molecular simulations to evaluate the relevant quantities entering in this equation. This approach could, for example, be used to investigate the nanoscale capillary freezing of ionic liquids recently observed experimentally between the tip of an atomic force microscope and a substrate.